Tabla de propiedades

Apndice A

PPPPPPPPRRRRRRRROOOOOOOOPPPPPPPPIIIIIIIIEEEEEEEEDDDDDDDDAAAAAAAADDDDDDDDEEEEEEEESSSSSSSS

LLIISSTTAA DDEE TTAABBLLAASS

A.1 Constantes Fsicas A.2a Constante particular y calor molar a presin constante de algunas sustancias gaseosas

comunes A.2b Calor molar de algunas sustancias lquidas comunes. A.2c Calor molar de algunas sustancias slidas comunes. A.3 Masa molar, propiedades crticas y factor acntrico de algunas sustancias comunes. A.4a Valores del parmetro de Lee y Kesler 0Z . A.4b Valores del parmetro de Lee y Kesler 1Z . A.5a Valores del parmetro de Lee y Kesler 0hZ . A.5b Valores del parmetro de Lee y Kesler 1hZ . A.6a Valores del parmetro de Lee y Kesler 0sZ . A.6b Valores del parmetro de Lee y Kesler 1sZ . A.7 Equilibrio de fases lquido vapor para algunas sustancias comunes. A.8 Propiedades del agua saturada: tabla de temperatura A.9 Propiedades del agua saturada: tabla de presin A.10 Propiedades del agua: tabla de vapor sobrecalentado A.11 Propiedades del agua: tabla de lquido comprimido A.12 Propiedades del hielo saturado A.13 Propiedades del aire como gas ideal A.14 Masa molar, entalpa y funcin de Gibbs de formacin y entropa absoluta para una

seleccin de sustancias a 298 K y 1 atm A.15 Poder calorfico inferior, calor de vaporizacin, volumen molar y punto de ebullicin

normal de algunos combustibles a 298 K y 1 atm A.16 Entalpa y energa interna sensibles y entropa absoluta del CO2 como gas ideal A.17 Entalpa y energa interna sensibles y entropa absoluta del CO como gas ideal A.18 Entalpa y energa interna sensibles y entropa absoluta del H2O como gas ideal

TERMODINMICA APLICADA 754

A.19 Entalpa y energa interna sensibles y entropa absoluta del H2 como gas ideal A.20 Entalpa y energa interna sensibles y entropa absoluta del O2 como gas ideal A.21 Entalpa y energa interna sensibles y entropa absoluta del N2 como gas ideal A.22 Entalpa sensible de algunos combustibles gaseosos a baja presin A.23 Logaritmos en base 10 de la constante de equilibrio Kp para algunas reacciones A.24 Flujo isoentrpico unidimensional de un gas ideal con k=1.4 A.25 Flujo unidimensional a travs de un shock normal de un gas ideal con k=1.4

APNDICE A 755

TTAABBLLAA AA..11

Constantes fsicas*

Nombre Smbolo Valor y unidades Velocidad de la luz c 2.9979108 m/s2

Constante de Planck h 6.626071034 J s/partcula Nmero de Avogadro NNNN 6.02211023 partculas/mol

Constante de Faraday FFFF 96467.7 C/mol

Carga del protn e=FFFF/NNNN 1.60221019 C Constante universal de los gases RRRR 8.314472 J/mol K Constante de Boltzmann k=RRRR/NNNN 1.380651023 J/partcula K Aceleracin de la gravedad estndar g 9.80665 m/s2

Presin atmsfrica estndar p 101325 Pa * Fuente: Committee on Data for Science and Technology, 2002.


TTAABBLLAA AA..22aa

Constante particular y calor molar de algunas sustancias gaseosas comunes* R en J/kg K. Constantes para la ecuacin 22/ ++++++++++++==== dTcTbTac p RRRR , en donde 298TTmax , K

Sustancia Frmula R Tmax a b103 c106 d105 Acetileno C2H2 319.3 1500 6.132 1.952 1.299 Acido clorhdrico HCl 228.0 2000 3.156 0.623 0.151 Acido sulfhdrico H2S 244.0 2300 3.931 1.490 0.232 Agua H2O 461.5 2000 3.470 1.450 0.121 Aire 287.0 2000 3.355 0.575

0.016 Amonaco NH3 488.2 1800 3.578 3.020 0.186 Bixido de azufre SO2 129.8 2000 5.699 0.801 1.015 Bixido de carbono CO2 188.9 2000 5.457 1.045 1.157 Bixido de nitrgeno NO2 180.7 2000 4.982 1.195 0.792 Bisulfuro de carbono CS2 109.2 1800 6.311 0.805 0.906 Butano C4H10 143.1 1500 1.935 36.915 11.402 Cloro Cl2 117.3 3000 4.442 0.089 0.344 Etano C2H6 276.5 1500 1.131 19.225 5.561 Etanol C2H6O 180.5 1500 3.518 20.001 6.002 Hidrgeno H2 4125 3000 3.249 0.422 0.083 Metano CH4 518.3 1500 1.702 9.081 2.164 Metanol CH4O 259.5 1500 2.211 12.216 3.450 Monxido de carbono CO 296.8 2500 3.376 0.557

0.031 Nitrgeno N2 296.8 2000 3.280 0.593 0.040 xido ntrico NO 277.1 2000 3.387 0.629 0.014 xido nitroso N2O 188.9 2000 5.328 1.214 0.928 Oxgeno O2 259.8 2000 3.639 0.506 0.227 Propano C3H6 188.6 1500 1.213 28.785 8.824 Trixido de azufre SO3 103.9 2000 8.060 1.056 2.028

* Adaptada de P. FERNANDEZ DEZ, Termodinmica tcnica, Universidad de Cantabria.

APNDICE A 757

TTAABBLLAA AA..22bb

Calor molar de algunas sustancias lquidas comunes* Constantes para la ecuacin 2/ cTbTac p ++++++++====RRRR , en donde 273 KT373 K

Sustancia Frmula a b103 c106

Agua H2O 8.712 1.25 0.18 Amonaco NH3 22.626 100.75 192.71 Anilina 15.819 29.03 15.80 Benceno C6H6 0.747 67.96 37.78 Cicloexano C6H12 9.048 141.38 161.62 Clorobenceno 11.278 32.86

31.90 Cloroformo 19.215

42.89 83.01 Etanol C2H6O 33.866 172.60 349.17 Metanol CH4O 13.431 51.28 131.13 Propanol C3H8O 41.653 210.32 427.20 Tetracloruro de carbono CCl4 21.155 48.28 101.14 Tolueno C7H8 15.133 6.79 16.35 Trixido de azufre SO3 2.930 137.08 84.73



TTAABBLLAA AA..22cc

Calor molar de algunas sustancias slidas comunes* Constantes para la ecuacin 2/ ++++++++==== cTbTac p RRRR , en donde 298 KTTmax , K

Sustancia Tmax a b103 c105

CaO 2000 6.104 0.443 1.047

CaCO3 1200 12.572 2.637 3.120 CaCl2 1055 8.646 1.530 0.302 C (grafito) 2000 1.771 0.771

0.867 Cu 1357 2.677 0.815 0.035 CuO 1400 5.780 0.973

0.874 Fe () 1043

0.111 6.111 1.150 Fe2O3 960 11.812 9.697 1.976 FeS 411 2.612 13.286 I2 386.8 6.481 1.502 Na 371 1.988 4.688 NaCl 1073 5.526 1.963 NaOH 566 0.121 16.316 1.948 S (rmbico) 368.3 4.114

1.728 0.783 SiO2 (cuarzo) 847 4.871 5.365 1.001


APNDICE A 759

TTAABBLLAA AA..33

Masa molar, propiedades crticas y factor acntrico de algunas sustancias comunes* M, g/mol; Tc , K; pc , bar; cv , m3/mol

Sustancia M pc Tc 610cv Acetileno 26.0378 61.4 308.3 112.7 0.184 Agua 18.0152 220.9 647 56.8 0.344 Aire 28.9700 37.7 132.5 88.3 Argn 39.9480 48.6 150.8 75.2

0.004 Azufre 32.0600 Benceno 78.1134 49.2 562 260.4 0.212 Bixido de Azufre 64.0588 78.8 430.7 121.8 0.251 Bixido de Carbono 44.0098 73.8 304.2 94.3 0.225 Bixido de nitrgeno 46.0055 101.0 431 167.8 Cloro 35.4530 Butano 58.1230 38.0 425.2 254.7 0.193 Etano 30.0694 48.8 305.5 148.0 0.098 Etanol 46.0634 63.8 516 167.3 0.635 Diclorodifluorometano (R12) 120.9138 40.1 384.7 217.9 0.176 Fluor 18.9984 Helio 4.0026 2.29 5.3 57.8

0.387 Heptano 100.2034 27.35 540.17 410.8 0.351 Hexano 86.1766 30.3 507.9 367.8 0.296 Hidrgeno 1.0079 13.0 33.3 65.0

0.220 Metano 16.0426 46.4 191.1 99.0 0.008 Metanol 32.0420 79.5 513.2 118.0 0.559 Monxido de carbono 28.0104 34.9 113 93.0 0.049 Monxido de nitrgeno 30.0061 64.8 180 57.7 0.607 Nen 20.1790 27.2 44.5 41.7 0.000 Nitrgeno 14.0067 33.9 126.2 90.1 0.040 n-Octano 114.2302 24.98 569.4 490.1 0.394 Oxgeno 15.9994 50.8 154.8 78.0 0.021 n-Pentano 72.1498 33.47 470.3 310.3 0.251 Propano 44.0962 42.5 369.8 203.0 0.152 Tetracloruro de carbono 153.8230 45.6 556.4 275.9 0.194 Tetrafluoroetano (R134a) 40.67 374.3 184.7

* Fuente: HOWELL, J. y BUCKIUS, R., Principios de termodinmica para ingenieros, McGraw Hill, 1990.


TTAABBLLAA AA..44aa

Valores del parmetro de Lee y Kesler Z0

pr Tr

0.1 0.2 0.4 0.6 0.8 1.0 1.2 1.5 2.0 3.0

0.3 0.0290 0.0579 0.1158 0.1737 0.2315 0.2892 0.3470 0.4335 0.5775 0.8648 0.4 0.0239 0.0477 0.0953 0.1429 0.1904 0.2379 0.2853 0.3563 0.4744 0.7095 0.5 0.0207 0.0413 0.0825 0.1236 0.1647 0.2056 0.2465 0.3077 0.4092 0.6110 0.6 0.0186 0.0371 0.0741 0.1109 0.1476 0.1842 0.2207 0.2753 0.3657 0.5446 0.7 0.8958 0.0344 0.0687 0.1027 0.1366 0.1703 0.2038 0.2538 0.3364 0.4991 0.8 0.9319 0.8539 0.0661 0.0985 0.1307 0.1626 0.1942 0.2411 0.3182 0.4690 0.9 0.9528 0.9015 0.7800 0.1006 0.1321 0.1630 0.1935 0.2383 0.3114 0.4257

0.95 0.9600 0.9174 0.8206 0.6967 0.1410 0.1705 0.1998 0.2432 0.3138 0.4501 1.0 0.9659 0.9300 0.8509 0.7574 0.6353 0.2901 0.2237 0.2583 0.3229 0.4522 1.1 0.9747 0.9485 0.8930 0.8323 0.7649 0.6880 0.5984 0.4580 0.3953 0.4770 1.2 0.9808 0.9611 0.9205 0.8779 0.8330 0.7858 0.7363 0.6605 0.5605 0.5425 1.3 0.9852 0.9702 0.9396 0.9083 0.8764 0.8438 0.8111 0.7624 0.6908 0.6344 1.4 0.9884 0.9768 0.9534 0.9298 0.9062 0.8827 0.8595 0.8256 0.7753 0.7202 1.5 0.9909 0.9818 0.9636 0.9456 0.9278 0.9103 0.8933 0.8689 0.8328 0.7887 1.6 0.9928 0.9856 0.9714 0.9575 0.9439 0.9308 0.9180 0.9000 0.8738 0.8410 1.8 0.9955 0.9910 0.9823 0.9739 0.9659 0.9583 0.9511 0.9413 0.9275 0.9118 2.0 0.9972 0.9944 0.9892 0.9842 0.9796 0.9754 0.9715 0.9664 0.9599 0.9550 2.2 0.9983 0.9967 0.9937 0.9910 0.9886 0.9965 0.9847 0.9826 0.9806 0.9827 2.4 0.9991 0.9983 0.9969 0.9957 0.9948 0.9941 0.9936 0.9935 0.9945 1.0011 2.6 0.9997 0.9994 0.9991 0.9990 0.9990 0.9993 0.9998 1.0010 1.0040 1.0137 2.8 1.0001 1.0002 1.0007 1.0013 1.0021 1.0031 1.0042 1.0063 1.0106 1.0223 3.0 1.0004 1.0008 1.0018 1.0030 1.0043 1.0057 1.0074 1.0101 1.0153 1.0284 3.5 1.0008 1.0017 1.0035 1.0055 1.0075 1.0097 1.0120 1.0156 1.0221 1.0368 4.0 1.0010 1.0021 1.0043 1.0066 1.0090 1.0115 1.0140 1.0179 1.0249 1.0401

* Fuente: A. BEJAN, Advanced engineering thermodynamics, John Wiley, 1988, table A.1.

APNDICE A 761

TTAABBLLAA AA..44bb

Valores del parmetro de Lee y Kesler Z1

pr Tr

0.1 0.2 0.4 0.6 0.8 1.0 1.2 1.5 2.0 3.0

0.3 0.0081 0.0161 0.00323 0.0484 0.0645 0.0806 0.0966 0.1207 0.1608 0.2407 0.4 0.0095 0.0190 0.0380 0.0570 0.0758 0.0946 0.1134 0.1414 0.1879 0.2799 0.5 0.0090 0.0181 0.0360 0.0539 0.0716 0.0893 0.1069 0.1330 0.1762 0.2611 0.6 0.0082 0.0164 0.0326 0.0487 0.0646 0.0803 0.0960 0.1192 0.1572 0.2312 0.7 0.1161 0.0148 0.0294 0.0438 0.0579 0.0718 0.0855 0.1057 0.1385 0.2013 0.8 0.0487 0.1160 0.0272 0.0401 0.0526 0.0648 0.0767 0.0940 0.1217 0.1736 0.9 0.0205 0.0442 0.1118 0.0396 0.0503 0.0604 0.0701 0.0840 0.1059 0.1463

0.95 0.0126 0.0262 0.0589 0.1110 0.0540 0.0607 0.0678 0.0788 0.0967 0.1310 1.0 0.0069 0.0140 0.0285 0.0435 0.0588 0.0879 0.0609 0.0678 0.0824 0.1118 1.1 0.0001 0.0007 0.0038 0.0106 0.0236 0.0476 0.0897 0.1630 0.0698 0.0373 1.2 0.0039 0.0084 0.0190 0.0326 0.0499 0.0719 0.0991 0.1477 0.1990 0.1095 1.3 0.0061 0.0125 0.0267 0.0429 0.0612 0.0819 0.1048 0.1420 0.1991 0.2079 1.4 0.0072 0.0147 0.0306 0.0477 0.0661 0.0857 0.1063 0.1383 0.1894 0.2397 1.5 0.0078 0.0158 0.0323 0.0497 0.0677 0.0864 0.1055 0.1345 0.1806 0.2433 1.6 0.0080 0.0162 0.0330 0.0501 0.0677 0.0855 0.1035 0.1303 0.1279 0.2381 1.8 0.0081 0.0162 0.0325 0.0488 0.0652 0.0816 0.0978 0.1216 0.1593 0.2224 2.0 0.0078 0.0155 0.0310 0.0464 0.0617 0.0767 0.0916 0.1133 0.1476 0.2069 2.2 0.0074 0.0147 0.0293 0.0437 0.0579 0.0719 0.0857 0.1057 0.1374 0.1932 2.4 0.0070 0.0139 0.0276 0.0411 0.0544 0.0675 0.0803 0.0989 0.1285 0.1812 2.6 0.0066 0.0131 0.0260 0.0387 0.0512 0.0634 0.0754 0.0929 0.1207 0.1706 2.8 0.0062 0.0124 0.0245 0.0365 0.0483 0.0598 0.0711 0.0876 0.1138 0.1613 3.0 0.0059 0.0117 0.0232 0.0345 0.0456 0.0565 0.0672 0.0828 0.1076 0.1529 3.5 0.0052 0.0103 0.0204 0.0303 0.0401 0.0497 0.0591 0.0728 0.0949 0.1356 4.0 0.0046 0.0091 0.0182 0.0270 0.0357 0.0433 0.0527 0.0651 0.0849 0.1219



TTAABBLLAA AA..55aa

Valores del parmetro de Lee y Kesler 0hZ

pr Tr

0.1 0.2 0.4 0.6 0.8 1.0 1.2 1.5 2.0 3.0

0.3 6.040 6.034 6.022 6.011 5.999 5.987 5.975 5.975 5.927 5.868 0.4 5.757 5.751 5.738 5.726 5.713 5.700 5.687 5.668 5.636 5.572 0.5 5.459 5.453 5.440 5.427 5.414 5.401 5.388 5.369 5.336 5.270 0.6 5.159 5.153 5.141 5.129 5.116 5.104 5.091 5.073 5.041 4.976 0.7 0.213 4.848 4.838 4.828 4.818 4.808 4.797 4.781 4.752 4.693 0.8 0.160 0.345 4.507 4.504 4.499 4.494 4.488 4.478 4.459 4.413 0.9 0.126 0.264 0.596 4.074 4.094 4.108 4.118 4.127 4.132 4.119

0.95 0.113 0.235 0.516 0.885 3.763 3.825 3.865 3.904 3.940 3.958 1.0 0.103 0.212 0.455 0.750 1.151 2.584 3.441 3.598 3.706 3.782 1.1 0.086 0.175 0.367 0.581 0.827 1.120 1.487 2.203 2.965 3.353 1.2 0.073 0.148 0.305 0.474 0.657 0.857 1.076 1.443 2.079 2.807 1.3 0.063 0.127 0.259 0.399 0.545 0.698 0.860 1.116 1.560 2.274 1.4 0.055 0.110 0.224 0.341 0.463 0.588 0.716 0.915 1.253 1.857 1.5 0.048 0.097 0.196 0.297 0.400 0.505 0.611 0.774 1.046 1.549 1.6 0.043 0.086 0.173 0.261 0.350 0.440 0.531 0.667 0.894 1.318 1.8 0.034 0.068 0.137 0.206 0.275 0.344 0.413 0.515 0.683 0.996 2.0 0.028 0.056 0.111 0.167 0.222 0.276 0.330 0.411 0.541 0.782 2.2 0.023 0.046 0.092 0.137 0.182 0.226 0.269 0.334 0.437 0.629 2.4 0.019 0.038 0.076 0.114 0.150 0.187 0.222 0.275 0.359 0.513 2.6 0.016 0.032 0.064 0.095 0.125 0.155 0.185 0.228 0.297 0.422 2.8 0.014 0.027 0.054 0.080 0.105 0.130 0.154 0.190 0.246 0.348 3.0 0.011 0.023 0.045 0.067 0.088 0.109 0.129 0.159 0.205 0.288 3.5 0.007 0.015 0.029 0.043 0.056 0.069 0.081 0.099 0.127 0.174 4.0 0.005 0.009 0.017 0.026 0.033 0.041 0.048 0.058 0.072 0.095


APNDICE A 763

TTAABBLLAA AA..55bb

Valores del parmetro de Lee y Kesler 1hZ

pr Tr

0.1 0.2 0.4 0.6 0.8 1.0 1.2 1.5 2.0 3.0

0.3 11.095 11.091 11.083 11.076 11.069 11.062 11.055 11.044 11.027 10.992 0.4 10.121 10.120 10.121 10.121 10.121 10.121 10.121 10.121 10.122 10.123 0.5 8.870 8.872 8.876 8.880 8.884 8.888 8.892 8.899 8.909 8.932 0.6 7.570 7.573 7.579 7.585 7.591 7.596 7.603 7.614 7.632 7.669 0.7 0.415 6.360 6.367 6.373 6.381 6.388 6.395 6.407 6.429 6.475 0.8 0.234 0.542 5.266 5.271 5.278 5.285 5.293 5.306 5.330 5.385 0.9 0.144 0.308 0.751 4.254 4.248 4.249 4.255 4.268 4.298 4.371

0.95 0.115 0.241 0.542 0.994 3.737 3.712 3.713 3.730 3.773 3.873 1.0 0.093 0.191 0.410 0.675 1.034 2.471 2.952 3.065 3.186 3.358 1.1 0.061 0.123 0.251 0.381 0.507 0.617 0.673 0.617 1.261 2.167 1.2 0.040 0.080 0.158 0.232 0.297 0.349 0.381 0.381 0.361 0.934 1.3 0.026 0.052 0.100 0.142 0.177 0.203 0.218 0.218 0.178 0.300 1.4 0.016 0.032 0.060 0.083 0.100 0.111 0.115 0.108 0.070 0.044 1.5 0.009 0.018 0.032 0.042 0.048 0.049 0.046 0.032 0.008 0.078 1.6 0.004 0.007 0.012 0.013 0.011 0.005 0.004 0.023 0.065 0.151 1.8 0.003 0.006 0.015 0.025 0.037 0.051 0.067 0.094 0.143 0.241 2.0 0.007 0.015 0.030 0.047 0.065 0.085 0.105 0.136 0.190 0.295 2.2 0.010 0.020 0.040 0.062 0.083 0.106 0.128 0.163 0.221 0.331 2.4 0.012 0.023 0.047 0.071 0.095 0.120 0.144 0.181 0.242 0.356 2.6 0.013 0.026 0.052 0.078 0.104 0.130 0.156 0.194 0.257 0.376 2.8 0.014 0.028 0.055 0.082 0.110 0.137 0.164 0.204 0.269 0.391 3.0 0.014 0.029 0.058 0.086 0.114 0.142 0.170 0.211 0.278 0.403 3.5 0.016 0.031 0.062 0.092 0.122 0.152 0.181 0.224 0.294 0.425 4.0 0.016 0.032 0.064 0.096 0.127 0.158 0.188 0.233 0.306 0.442



TTAABBLLAA AA..66aa

Valores del parmetro de Lee y Kesler 0sZ

pr Tr

0.1 0.2 0.4 0.6 0.8 1.0 1.2 1.5 2.0 3.0

0.3 9.319 8.635 7.961 7.574 7.304 7.099 6.935 6.740 6.497 6.182 0.4 8.506 7.821 7.144 6.755 6.483 6.275 6.109 5.909 5.660 5.330 0.5 7.481 7.156 6.479 6.089 5.816 5.608 5.441 5.240 4.989 4.656 0.6 7.294 6.610 5.933 5.544 5.273 5.066 4.900 4.700 4.451 4.120 0.7 0.206 6.140 5.467 5.082 4.814 4.610 4.446 4.250 4.007 3.684 0.8 0.134 0.294 5.026 4.649 4.388 4.191 4.034 3.846 3.615 3.310 0.9 0.094 0.199 0.463 4.145 3.912 3.738 3.599 3.434 3.231 2.964

0.95 0.080 0.168 0.377 0.671 3.556 3.433 3.326 3.193 3.023 2.790 1.0 0.069 0.144 0.315 0.532 0.847 2.178 2.893 2.879 2.784 2.609 1.1 0.053 0.108 0.230 0.371 0.537 0.742 1.012 1.557 2.081 2.202 1.2 0.042 0.085 0.177 0.277 0.389 0.512 0.651 0.890 1.308 1.727 1.3 0.033 0.068 0.140 0.217 0.298 0.385 0.478 0.628 0.891 1.299 1.4 0.027 0.056 0.114 0.174 0.237 0.303 0.372 0.478 0.663 0.990 1.5 0.023 0.046 0.094 0.143 0.194 0.246 0.299 0.381 0.520 0.777 1.6 0.019 0.039 0.079 0.120 0.162 0.204 0.247 0.312 0.421 0.628 1.8 0.014 0.029 0.058 0.088 0.117 0.147 0.177 0.222 0.296 0.438 2.0 0.011 0.022 0.044 0.067 0.089 0.111 0.134 0.167 0.221 0.325 2.2 0.009 0.018 0.035 0.053 0.070 0.087 0.105 0.130 0.172 0.251 2.4 0.007 0.014 0.028 0.042 0.056 0.070 0.084 0.104 0.138 0.201 2.6 0.006 0.012 0.023 0.035 0.046 0.058 0.069 0.086 0.113 0.164 2.8 0.005 0.010 0.020 0.029 0.039 0.048 0.058 0.072 0.094 0.137 3.0 0.004 0.008 0.017 0.025 0.033 0.041 0.049 0.061 0.080 0.116 3.5 0.003 0.006 0.012 0.017 0.023 0.029 0.034 0.042 0.056 0.081 4.0 0.002 0.004 0.009 0.013 0.017 0.021 0.025 0.031 0.041 0.059


APNDICE A 765

TTAABBLLAA AA..66bb

Valores del parmetro de Lee y Kesler 1sZ

pr Tr

0.1 0.2 0.4 0.6 0.8 1.0 1.2 1.5 2.0 3.0

0.3 16.764 16.744 16.705 16.665 16.626 16.586 16.547 16.488 16.390 16.195 0.4 13.981 13.972 13.953 13.934 13.915 13.896 13.877 13.849 13.803 13.714 0.5 11.197 11.192 11.182 11.172 11.162 11.153 11.143 11.129 11.107 11.063 0.6 8.826 8.823 8.817 8.811 8.806 8.799 8.794 8.787 8.777 8.760 0.7 0.491 6.951 6.945 6.941 6.937 6.933 6.930 6.926 6.922 6.919 0.8 0.246 0.578 5.475 5.468 5.462 5.458 5.455 5.453 5.452 5.461 0.9 0.140 0.301 0.744 4.269 4.249 4.238 4.232 4.230 4.236 4.267

0.95 0.109 0.228 0.517 0.961 3.697 3.658 3.647 3.648 3.669 3.728 1.0 0.086 0.177 0.382 0.632 0.977 2.399 2.868 2.967 3.067 3.200 1.1 0.055 0.112 0.229 0.350 0.470 0.577 0.640 0.618 1.241 2.067 1.2 0.037 0.075 0.149 0.220 0.286 0.343 0.385 0.412 0.447 0.991 1.3 0.026 0.052 0.102 0.148 0.190 0.226 0.254 0.282 0.300 0.481 1.4 0.019 0.037 0.072 0.104 0.133 0.158 0.178 0.200 0.220 0.290 1.5 0.014 0.027 0.053 0.076 0.097 0.115 0.130 0.147 0.166 0.206 1.6 0.011 0.021 0.040 0.057 0.073 0.086 0.098 0.112 0.129 0.159 1.8 0.006 0.013 0.024 0.035 0.044 0.053 0.060 0.070 0.083 0.105 2.0 0.005 0.010 0.019 0.028 0.036 0.043 0.049 0.057 0.069 0.089 2.2 0.003 0.006 0.011 0.016 0.021 0.025 0.029 0.035 0.043 0.060 2.4 0.002 0.004 0.008 0.012 0.015 0.019 0.022 0.027 0.034 0.048 2.6 0.002 0.003 0.006 0.009 0.012 0.015 0.018 0.021 0.028 0.041 2.8 0.001 0.003 0.005 0.008 0.010 0.012 0.014 0.018 0.023 0.035 3.0 0.001 0.002 0.004 0.006 0.008 0.010 0.012 0.015 0.020 0.031 3.5 0.001 0.001 0.003 0.004 0.006 0.007 0.009 0.011 0.015 0.024 4.0 0.001 0.001 0.002 0.003 0.005 0.006 0.007 0.009 0.012 0.020



TTAABBLLAA AA..77

Equilibrio de fases lquido - vapor para algunas sustancias comunes*

Constantes para la ecuacin cT

bap

++++====*log . T en K y p*en kPa.

Sustancia Frmula Tmin-Tmax a b c Monxido de C CO

210 165 13.8722 769.93 1.6369 Bixido de C CO2 119 69 15.3768 1956.25 2.1117 Metano CH4 181 152 13.5840 968.13 3.7200 Metanol CH4O 16 91 16.4948 3593.39 35.2249 Acetileno C2H2 129 83 14.8321 1836.66 8.4521 Etano C2H6 143 75 13.8797 1582.18 13.7622 Etanol C2H6O 3 96 16.1952 3423.53 55.7152 Acetona C3H6O 32 77 14.7171 2975.95 345228 Propano C3H8 108 25 13.7097 1872.82 25.1011 Isopropanol C3H8O 12 127 15.6491 3109.34 73.5459 n-Butano C4H10 78 19 13.9836 2292.44 27.8623 2 metilpropano (isobutano) C4H10 87 7 13.8137 2150.23 27.6228 Butanol C4H10O 15 131 14.6961 2902.96 102.9116 Ciclopentano C5H10 40 72 13.8440 2590.03 41.6716 n-Pentano C5H12 50 58 13.9778 2554.60 36.2529 2 metilbutano (isopentano) C5H12 57 49 13.6106 2345.09 40.2128 Benceno C6H6 16 104 14.1603 2948.78 44.5633 n-Exano C6H14 25 92 14.0568 2825.42 42.7089 Tolueno C7H8 6 136 14.2515 3242.38 47.1806 n-Heptano C7H16 2 123 13.9008 2932.72 55.6356 n-Octano C8H18 19 152 14.2368 3304.16 55.2278 n-Nonano C9H20 39 179 13.9548 3290.56 71.5056 n-Decano C10H22 58 203 13.9899 3452.22 78.8993 n-Undecano C11H24 75 226 14.7851 4152.92 60.4933 n-Dodecano C12H26 91 247 14.0587 3744.01 92.8311

APNDICE A 767

TABLA A7 (Continuacin)

Sustancia Frmula Tmin-Tmax a b c 1 metilnaftaleno C11H10 108 278 7.03592 1826.948 195.002 Tridecano C13H28 107 267 7.00756 1690.670 174.220 Tetradecano C14H30 122 286 7.01300 1740.880 167.720 Pentadecano C15H32 136 304 7.02359 1789.950 161.380 Hexadecano (cetano) C16H34 149 321 7.02867 1830.510 154.450 Heptadecano C17H36 161 337 7.01430 1865.100 149.200 Octadecano C18H38 172 352 7.00220 1894.300 143.300 Nonadecano C19H40 184 366 7.01530 1932.800 137.600 Eicosano C20H42 198 379 7.15220 2032.700 132.100

* Tomada de http://www.engr.umd.edu/~nsw/ench250/antoine.dat


TTAABBLLAA AA..88

Propiedades del agua saturada: tabla de temperatura

, kg/m3 ; v, m3/kg; h, kJ/kg; s, kJ/kg/K

T, C p, bar ' v" h' h" s' s" 0.01 0.006108 999.80 206.3 0.00 2501 0.0000 9.1544 2 0.007054 999.90 179.9 8.42 2504 0.0306 9.1018 4 0.008129 999.90 157.3 16.84 2508 0.0610 9.0498 5 0.008719 999.90 147.2 21.05 2510 0.0762 9.0241 6 0.009347 999.90 137.8 25.25 2512 0.0913 8.9978 7 0.010013 999.90 129.1 29.45 2514 0.1063 8.9736 8 0.010721 999.80 121.0 33.55 2516 0.1212 8.9485 9 0.011473 999.70 113.4 37.85 2517 0.1361 8.9238

10 0.012277 999.60 106.42 42.04 2519 0.1510 8.8994 11 0.013118 999.50 99.91 46.22 2521 0.1658 8.8752 12 0.014016 999.40 93.84 50.41 2523 0.1805 8.8513 13 0.014967 999.30 88.18 54.60 2525 0.1952 8.8276 14 0.015974 999.20 82.90 58.78 2527 0.2098 8.8040 15 0.017041 999.00 77.97 62.97 2528 0.2244 8.7806 16 0.018170 998.90 73.39 67.16 2530 0.2389 8.7574 17 0.019364 998.70 69.10 71.34 2532 0.2534 8.7344 18 0.02062 998.50 65.09 75.53 2534 0.2678 8.7116 19 0.02196 998.40 61.34 79.72 2536 0.2821 8.6890 20 0.02337 998.20 57.84 83.90 2537 0.2964 8.6665 21 0.02486 997.90 54.56 88.09 2539 0.3107 8.6442 22 0.02643 997.71 51.50 92.27 2541 0.3249 8.6220 23 0.02808 997.51 48.62 96.46 2543 0.3391 8.6001 24 0.02982 997.21 45.93 100.63 2545 0.3532 8.5785 25 0.03166 997.01 43.40 104.81 2547 0.3672 8.5570 26 0.03360 996.71 41.04 108.99 2548 0.3812 8.5358 27 0.03564 996.41 38.82 113.17 2550 0.3951 8.5147 28 0.03779 996.21 36.73 117.35 2552 0.4090 8.4938 29 0.04004 995.92 34.77 121.53 2554 0.4228 8.4730 30 0.04241 995.62 32.93 125.71 2556 0.4366 8.4523 31 0.04491 995.32 31.20 129.89 2558 0.4503 8.4319 32 0.04753 994.93 29.57 134.07 2559 0.4640 8.4117 33 0.05029 994.63 28.04 138.25 2561 0.4777 8.3916 34 0.05318 994.33 26.60 142.42 2563 0.4913 8.3716 35 0.05622 993.94 25.24 146.60 2565 0.5049 8.3519 36 0.05940 993.64 23.97 150.78 2567 0.5185 8.3323 37 0.06274 993.25 22.77 154.96 2569 0.5320 8.3129 38 0.06624 992.95 21.63 159.14 2570 0.5455 8.2938 39 0.06991 992.56 20.56 163.32 2572 0.5589 8.2748 40 0.07375 992.16 19.55 167.50 2574 0.5723 8.2559

APNDICE A 769

TABLA A.8 (Continuacin)

T, C p, bar ' v" h' h" s' s" 45 0.09584 990.20 15.28 188.40 2582 0.6384 8.1638 50 0.12335 988.04 12.04 209.3 2592 0.7038 8.0753 55 0.15740 985.71 9.578 230.2 2600 0.7679 7.9901 60 0.19917 983.19 7.678 251.1 2609 0.8311 7.9084 65 0.2501 980.49 6.201 272.1 2617 0.8934 7.8297 70 0.3117 977.71 5.045 293.0 2626 0.9549 7.7544 75 0.3855 974.85 4.133 314.0 2635 1.0157 7.6815 80 0.4736 971.82 3.408 334.9 2643 1.0753 7.6116 85 0.5781 968.62 2.828 355.9 2651 1.1342 7.5438 90 0.7011 965.34 2.361 377.0 2659 1.1925 7.4787 95 0.8451 961.91 1.982 398.0 2668 1.2502 7.4155

100 1.0131 958.31 1.673 419.1 2676 1.3071 7.3547 110 1.4326 951.02 1.210 461.3 2691 1.4184 7.2387 120 1.9854 943.13 0.8917 503.7 2706 1.5277 7.1298 130 2.7011 934.84 0.6683 546.3 2721 1.6354 7.0272 140 3.614 926.10 0.5087 589.0 2734 1.7392 6.9304 150 4.760 916.93 0.3926 632.2 2746 1.8418 6.8383 160 6.180 907.36 0.3068 675.6 2758 1.9427 6.7508 170 7.920 897.34 0.2426 719.2 2769 2.0417 6.6666 180 10.920 886.92 0.1939 763.1 2778 2.1395 6.5858 190 12.553 876.04 0.1564 807.5 2786 2.2357 6.5074 200 15.551 864.68 0.1272 852.4 2793 2.3308 6.4318 210 19.080 852.81 0.1043 897.7 2798 2.4246 6.3577 220 23.201 840.34 0.08606 943.7 2802 2.5179 6.2849 230 27.979 827.34 0.07147 990.4 2803 2.6101 6.2133 240 33.480 813.60 0.05967 1037.5 2803 2.7021 6.1425 250 39.776 799.23 0.05006 1085.7 2801 2.7934 6.0721 260 46.94 784.01 0.04215 1135.1 2796 2.8851 6.0013 270 55.05 767.87 0.03560 1185.3 2790 2.9764 5.9297 280 64.19 750.69 0.03013 1236.9 2780 3.0681 5.8573 290 74.45 732.33 0.02554 1290.0 2766 3.1611 5.7827 300 85.92 712.45 0.02164 1344.9 2749 3.2548 5.7049 320 112.90 667.11 0.01545 1462.1 2700 3.4495 5.5353 340 146.08 610.13 0.01078 1594.7 2622 3.6605 5.3361 360 186.74 527.98 0.00694 1762 2481 3.9162 5.0530 374.15 221.297 306.75 0.00326 2100 2100 4.4296 4.4296


TTAABBLLAA AA..99

Propiedades del agua saturada: tabla de presin , kg/m3 ; v, m3/kg; h, kJ/kg; s, kJ/kg/K

p, bar T, C ' v" h' h" s' s" 0.01 6.92 999.9 129.9 29.32 2513 0.1054 8.975 0.02 17.5 998.6 66.97 73.52 2533 0.2609 8.722 0.03 24.1 997.2 45.66 101.04 2545 0.3546 8.576 0.04 29.0 995.9 34.81 121.42 2554 0.4225 8.473 0.05 32.9 994.7 28.19 137.83 2561 0.4761 8.393 0.06 36.2 993.6 23.74 151.50 2567 0.5207 8.328 0.07 39.1 992.6 20.53 163.43 2572 0.5591 8.274 0.08 41.5 991.6 18.10 173.9 2576 0.5927 8.227 0.09 43.8 990.7 16.20 183.3 2580 0.6225 8.186 0.10 45.8 989.8 14.68 191.9 2584 0.6492 8.149 0.15 54.0 986.2 10.02 226.1 2599 0.7550 8.007 0.20 60.1 983.2 7.647 251.4 2609 0.8321 7.907 0.25 65.0 980.5 6.202 272.0 2618 0.8934 7.830 0.30 69.1 978.3 5.226 289.3 2625 0.9441 7.769 0.35 72.7 976.2 5.529 304.3 2631 0.9877 7.715 0.40 75.9 974.3 3.994 317.7 2636 1.0261 7.670 0.45 78.8 972.6 3.574 329.6 2641 1.0601 7.629 0.50 81.4 971.0 3.239 340.6 2645 1.0910 7.593 0.60 86.0 968.1 2.732 360.0 2653 1.1453 7.531 0.70 90.0 965.3 2.364 376.8 2660 1.1918 7.479 0.80 93.5 962.9 2.087 391.8 2665 1.2330 7.434 0.90 96.7 960.7 1.869 405.3 2670 1.2696 7.394 1.00 99.6 958.6 1.694 417.4 2675 1.3026 7.360 1.20 104.8 954.9 1.429 439.4 2683 1.3606 7.298 1.40 109.3 951.5 1.236 458.5 2690 1.4109 7.246 1.60 113.3 948.5 1.091 475.4 2696 1.4550 7.202 1.80 116.9 945.6 0.9773 490.7 2702 1.4943 7.163 2.00 120.2 943.0 0.8854 504.8 2707 1.5302 7.127 2.50 127.4 937.0 0.7185 535.4 2717 1.6071 7.053 3.00 133.5 931.7 0.6057 561.4 2725 1.672 6.992 3.50 138.9 927.1 0.5241 584.5 2732 1.728 6.941 4.00 143.6 922.8 0.4624 604.7 2738 1.777 6.897 4.50 147.9 918.9 0.4139 623.4 2744 1.821 6.857 5.00 151.8 915.2 0.3747 640.1 2749 1.860 6.822 6.00 158.8 908.5 0.3156 670.5 2757 1.931 6.761 7.00 165.0 902.4 0.2728 697.2 2764 1.992 6.709 8.00 170.4 896.9 0.2403 720.9 2769 2.046 6.663 9.00 175.4 891.8 0.2149 742.8 2774 2.094 6.623

10.0 179.9 887.1 0.1946 762.7 2778 2.138 6.587

APNDICE A 771


p, bar T, C ' v" h' h" s' s" 12.0 188.0 878.3 0.1633 798.3 2785 2.216 6.523 14.0 195.0 870.3 0.1408 830.0 2790 2.284 6.469 16.0 201.4 863.1 0.1238 858.3 2793 2.344 6.422 18.0 207.1 856.3 0.1104 884.4 2796 2.397 6.379 20.0 212.4 849.9 0.09958 908.5 2799 2.447 6.340 25.0 223.9 835.3 0.07993 961.8 2802 2.554 6.256 30.0 233.8 822.2 0.06665 1008.3 2804 2.646 6.186 35.0 242.5 810.0 0.05704 1049.8 2803 2.725 6.125 40.0 250.3 798.7 0.04977 1087.5 2801 2.796 6.070 45.0 257.4 788.0 0.04404 1122.1 2798 2.862 6.020 50.0 263.9 777.8 0.03944 1154.4 2794 2.921 5.973 60.0 275.6 758.4 0.03243 1213.9 2785 3.027 5.890 70.0 285.8 740.2 0.02737 1267.4 2772 3.122 5.814 80.0 295.0 722.6 0.02352 1317.0 2758 3.208 5.745 90.0 303.3 705.5 0.02048 1363.7 2743 3.287 5.678

100 311.0 688.7 0.01803 1407.7 2725 3.360 5.515 110 318.0 671.6 0.01598 1450.2 2705 3.430 5.553 120 324.6 654.9 0.01426 1491.1 2685 3.496 5.492 130 330.8 638.2 0.01277 1531.5 2662 3.561 5.432 140 336.6 620.7 0.01149 1570.8 2638 3.623 5.372 150 342.1 603.1 0.01035 1610 2611 3.684 5.310 160 347.3 584.8 0.009318 1650 2582 3.746 5.247 170 352.3 565.6 0.008382 1690 2548 3.807 5.177 180 357.0 544.4 0.007504 1732 2510 3.871 5.107 190 361.4 520.6 0.00668 1776 2466 3.938 5.027 200 365.7 490.2 0.00585 1827 2410 4.015 4.928 210 369.8 452.5 0.00498 1888 2336 4.108 4.803 221.9 374.15 306.75 0.00326 2100 2100 4.430 4.430


TTAABBLLAA AA..1100

Propiedades del agua: tabla de vapor sobrecalentado v, m3/kg; h, kJ/kg; s, kJ/kg/K

T, C v h s v h s v h s

0.05 bar (Tsat =32.9C) 0.10 bar (Tsat =45.8C) 0.20 bar (Tsat =60.1C) Sat. 28.19 2561 8.393 14.68 2584 8.149 7.647 2609 7.907

80 32.58 2650 8.659 16.27 2649 8.337 8.119 2648 8.015 120 36.28 2726 8.863 18.13 2726 8.542 9.049 2725 8.220 160 39.98 2803 9.047 19.98 2802 8.727 9.977 2801 8.406 200 43.68 2880 9.219 21.83 2879 8.897 10.905 2879 8.576 240 47.37 2958 9.376 23.68 2957 9.056 11.832 2957 8.735 280 51.07 3037 9.524 25.53 3037 9.203 12.758 3036 8.883 320 54.77 3117 9.664 27.38 3117 9.343 13.683 3117 9.023 360 58.47 3198 9.796 29.23 3198 9.475 14.606 3198 9.155 400 62.16 3280 9.921 31.08 3280 9.601 15.530 3280 9.281

0.50 bar (Tsat =81.4C) 1.0 bar (Tsat =99.6C) 2.0 bar (Tsat =120.2C) Sat. 3.239 2645 7.593 1.694 2675 7.360 0.8854 2707 7.127 160 3.982 2799 7.981 1.984 2796 7.654 0.9840 2790 7.324 200 4.355 2877 8.152 2.172 2875 7.828 1.080 2870 7.501 240 4.726 2956 8.311 2.359 2954 7.988 1.175 2950 7.663 280 5.098 3035 8.460 2.545 3033 8.139 1.269 3030 7.815 320 5.470 3116 8.599 2.731 3114 8.281 1.363 3111 7.957 360 5.841 3197 8.731 2.918 3195 8.414 1.457 3194 8.092 400 6.212 3279 8.858 3.102 3278 8.541 1.549 3276 8.219 440 6.582 3362 9.979 3.288 3361 8.661 1.641 3360 8.340 480 6.951 3447 9.095 3.472 3446 8.777 1.734 3445 8.456

5.0 bar (Tsat =151.8C) 10 bar (Tsat =188.0C) 20 bar (Tsat =212.4C) Sat. 0.3747 2749 6.822 0.1633 2785 6.523 0.0996 2799 6.340 240 0.4644 2937 7.224 0.2274 2918 6.877 0.1084 2875 6.491 280 0.5031 3020 7.380 0.2478 3005 7.040 0.1200 2972 6.674 320 0.5414 3104 7.525 0.2677 3091 7.189 0.1308 3065 6.837 360 0.5794 3188 7.662 0.2871 3177 7.330 0.1410 3156 6.985 400 0.6173 3272 7.791 0.3065 3263 7.460 0.1511 3246 7.122 440 0.6548 3356 7.913 0.3255 3349 7.585 0.1609 3335 7.251 480 0.6922 3441 8.030 0.3445 3435 7.703 0.1707 3423 7.371 520 0.7296 3527 8.141 0.3634 3522 7.817 0.1804 3512 7.486 560 0.7669 3614 8.249 0.3824 3609 7.924 0.1900 3600 7.596

APNDICE A 773


T, C v h s v h s v h s

30 bar (Tsat =233.8C) 40 bar (Tsat =250.3C) 60 bar (Tsat =275.6C) Sat. 0.0667 2804 6.186 0.0498 2801 6.070 0.0324 2785 5.890 320 0.0850 3038 6.615 0.0620 3010 6.446 0.0388 2948 6.177 360 0.0923 3135 6.773 0.0678 3113 6.613 0.0433 3067 6.371 400 0.0993 3229 6.916 0.0734 3211 6.762 0.0474 3174 6.535 440 0.1061 3321 7.048 0.0787 3306 6.900 0.0512 3275 6.681 480 0.1128 3411 7.172 0.0839 3399 7.027 0.0549 3373 6.815 520 0.1194 3501 7.289 0.0890 3491 7.146 0.0584 3469 6.939 560 0.1260 3592 7.400 0.0939 3583 7.259 0.0619 3564 7.056 600 0.1325 3682 7.506 0.0989 3674 7.367 0.0653 3658 7.165 640 0.1389 3773 7.608 0.1037 3766 7.470 0.0686 3751 7.271

80 bar (Tsat =295.0C) 100 bar (Tsat =318.0C) 150 bar (Tsat =342.1C) Sat. 0.0235 2758 5.745 0.0160 2705 5.553 0.0104 2611 5.310 360 0.0310 3017 6.177 0.0234 2958 6.002 0.0126 2765 5.559 400 0.0344 3135 6.358 0.0265 3093 6.207 0.0157 2973 5.878 440 0.0375 3244 6.515 0.0292 3211 6.377 0.0180 3123 6.093 480 0.0404 3347 6.657 0.0316 3320 6.527 0.0199 3248 6.268 520 0.0432 3447 6.785 0.0340 3424 6.662 0.0217 3364 6.419 560 0.0458 3544 6.905 0.0362 3524 6.786 0.0233 3472 6.554 600 0.0484 3640 7.019 0.0384 3621 6.901 0.0249 3576 6.677 640 0.0510 3736 7.126 0.0405 3719 7.011 0.0264 3680 6.794 680 0.0535 3832 7.230 0.0425 3818 7.116 0.0279 3784 6.903

200 bar 250 bar 300 bar 400 0.0100 2816 5.553 0.0060 2579 5.137 0.0028 2155 4.476 440 0.0122 3019 5.847 0.0087 2896 5.604 0.0062 2743 5.340 480 0.0140 3170 6.055 0.0104 3080 5.860 0.0080 2986 5.682 520 0.0155 3301 6.227 0.0118 3230 6.059 0.0093 3155 5.906 560 0.0169 3418 6.374 0.0130 3362 6.225 0.0104 3303 6.088 600 0.0182 3530 6.508 0.0141 3483 6.367 0.0144 3434 6.242 640 0.0194 3640 6.631 0.0152 3600 6.498 0.0124 3559 6.379 680 0.0205 3749 6.745 0.0162 3714 6.618 0.0132 3678 6.507 720 0.0217 3855 6.853 0.0171 3824 6.729 0.0141 3792 6.623 760 0.0228 3959 6.957 0.0180 3932 6.836 0.0149 3904 6.733


TTAABBLLAA AA..1111

Propiedades del agua: tabla de lquido comprimido , kg/m3 ; h, kJ/kg; s, kJ/kg/K

T, C h s v h s v h s

20 bar (Tsat =212.4C) 30 bar (Tsat =233.8C) 40 bar (Tsat =250.3C) 20 999.1 85.7 0.2957 999.6 86.7 0.2956 1000 87.6 0.2953 50 988.9 210.9 0.7020 989.4 211.8 0.7018 989.8 212.7 0.7012 80 972.8 336.2 1.0731 973.2 337.0 1.0726 973.7 337.8 1.0718

100 959.3 420.1 1.3048 959.8 420.9 1.3038 960.2 421.7 1.3030 120 944.0 504.7 1.5252 944.6 505.4 1.5244 945.0 506.2 1.5236 140 927.0 589.9 1.736 927.5 590.6 1.735 928.0 591.2 1.734 160 908.2 675.9 1.939 908.8 676.4 1.938 909.3 677.0 1.936 180 887.5 763.2 2.136 888.3 763.7 2.134 888.9 764.2 2.133 200 865.0 852.4 2.328 865.7 852.6 2.326 866.5 853.0 2.324 Sat. 849.9 908.5 2.447 822.2 1008 2.646 798.7 1088 2.796

50 bar (Tsat =263.9C) 100 bar (Tsat =318.0C) 150 bar (Tsat =342.1C) 50 990.3 213.6 0.7005 992.6 218.0 0.6980 994.6 222.3 0.6955 80 974.2 255.3 0.8273 976.1 342.9 1.0676 978.3 347.0 1.0641

100 960.8 422.5 1.3020 962.8 426.5 1.2982 965.3 430.4 1.2944 120 945.5 506.9 1.5223 947.7 510.5 1.5182 949.9 514.1 1.5139 140 928.6 591.9 1.733 931.0 595.3 1.728 933.4 598.7 1.723 160 909.9 677.7 1.935 912.7 681.0 1.929 915.3 684.2 1.923 180 889.5 764.9 2.131 892.8 768.0 2.123 895.6 770.8 2.117 200 867.3 853.6 2.322 870.9 856.0 2.314 874.2 858.3 2.306 240 815.4 1037 2.696 820.7 1038 2.684 824.9 1039 2.674 Sat. 777.8 1154 2.921 688.7 1408 3.360 603.1 1610 3.684

200 bar 250 bar 300 bar 100 967.2 434.2 1.2909 969.4 438.0 1.2873 971.5 441.9 1.2834 120 952.3 517.8 1.5098 954.7 521.5 1.5053 956.9 525.1 1.5014 140 936.0 602.1 1.719 938.6 605.6 1.714 941.1 609.0 1.709 160 918.2 687.4 1.919 921.0 690.5 1.914 923.8 693.6 1.908 180 898.8 773.5 2.112 902.0 776.3 2.107 905.0 779.1 2.100 200 877.7 860.6 2.299 881.1 863.0 2.293 884.6 865.4 2.287 240 829.5 1040 2.664 833.9 1042 2.655 838.2 1043 2.647 280 771.1 1231 3.023 777.4 1230 3.009 783.5 1230 2.996 320 692.5 1443 3.394 703.7 1437 3.371 712.8 1433 3.351 360 548.2 1739 3.876 590.0 1696 3.794 612.0 1676 3.747

APNDICE A 775

TTAABBLLAA AA..1122

Propiedades del hielo saturado*

, kg/m3 ; v, m3/kg; h, kJ/kg; s, kJ/kg/K

T, C p, Pa ' v" h' h" s' s" 0.01 611.7 916.8 206.0

334.3 2501 1.223 9.154 0 611.2 916.8 206.2

334.3 2500 1.223 9.155 2 518.0 917.1 241.6 338.5 2497 1.239 9.217 4 437.9 917.3 283.7 342.7 2493 1.255 9.281 6 369.3 917.6 334.1 346.8 2489 1.270 9.346 8 310.6 917.9 394.3 350.9 2486 1.286 9.412

10 260.0 918.2 466.6 355.0 2482 1.301 9.479 12 218.0 918.4 553.6 359.0 2478 1.317 9.548 14 181.9 918.8 658.7 363.0 2475 1.333 9.617 16 151.4 919.0 785.9 367.0 2471 1.348 9.688 18 125.6 919.3 940.4 371.0 2467 1.364 9.760 20 103.9 919.6 1128.5 374.9 2463 1.379 9.833 22 85.7 919.9 1358.3 378.8 2460 1.395 9.907 24 70.5 920.1 1640.0 382.7 2456 1.410 9.983 26 57.8 920.5 1986.3 386.5 2452 1.426 10.060 28 47.3 920.7 2413.6 390.4 2449 1.441 10.139 30 38.5 921.0 2942.9 394.1 2445 1.457 10.219 32 31.3 921.3 3599.9 397.9 2441 1.473 10.301 34 25.4 921.6 4418.9 401.6 2438 1.488 10.384 36 20.5 921.8 5443.9 405.3 2434 1.503 10.468 38 16.5 922.2 6730.9 409.0 2430 1.519 10.554 40 13.3 922.4 8353.9 412.6 2426 1.534 10.642

* Fuente: J.B. JONES Y R.E. DUGAN, Ingeniera Termodinmica, Prentice Hall, 1997


TTAABBLLAA AA..1133

Propiedades del aire como gas ideal.*

T, K; h y u, kJ/kg

T h u pr vr 250

48.20 120.0 0.239+0 2.735+0 298 0.00

85.53 1.000+0 1.000+0 300 1.98

84.13 1.012+0 9.9161 350 51.89

48.58 1.740+0 6.7271 400 102.3

12.47 2.795+0 4.7841 450 153.3 24.18 4.242+0 3.5301 500 204.9 61.37 6.239+0 2.6781 550 257.0 99.10 8.836+0 2.0821 600 309.6 137.4 1.217+1 1.6491 650 362.7 176.2 1.638+1 1.3271 700 416.4 215.5 2.162+1 1.0821 750 470.6 235.3 2.804+1 8.9422 800 525.3 295.7 3.587+1 7.4542 850 580.5 336.5 4.528+1 6.2762 900 636.2 377.9 5.648+1 5.3272 950 692.5 419.8 6.981+1 4.5532

1000 749.2 462.2 8.544+1 3.9152 1100 864.2 548.4 1.248+2 2.9472 1200 981.1 636.6 1.777+2 2.2592 1300 1100 726.7 2.469+2 1.7612 1400 1221 818.7 3.366+2 1.3912 1500 1343 912.5 4.512+2 1.1122 1600 1467 1008 5.957+2 8.9833 1700 1594 1106 7.765+2 7.3263 1800 1721 1205 1.000+3 6.0163 1900 1851 1306 1.276+3 4.9803 2000 1982 1408 1.613+3 4.1473

* Fuente: R.B. BIRD, W.E. STEWART, and E.N. LIGHTFOOT, Transport Phenomena, Wiley, 1960.

APNDICE A 777

TTAABBLLAA AA..1144

Masa molar, entalpa y funcin de Gibbs de formacin y entropa absoluta para una seleccin de sustancias a 298 K y 1 atm* M, g/mol; fh , kJ/mol; fg , kJ/mol; s , J/mol K

Sustancia Frmula M fh fg s Oxgeno O2(g) 31.999 0.0 0.00 205.0 Nitrgeno N2(g) 28.013 0.0 0.00 191.5 Hidrgeno H2(g) 2.016 0.0 0.00 130.6 Carbono C(s) 12.011 0.0 0.00 5.740 Azufre S(s) 32.06 0.0 0.00 31.8 Argon A 39.948 0.0 0.00 154.7 Helio He 4.0026 0.0 0.00 126.0 Monxido de C CO(g) 28.011

110.5 137.2 197.6 Bixido de C CO2(g) 44.011 393.5 394.4 213.6 Oxido ntrico NO 30.006 90.25 86.57 210.7 Bixido de S SO2(g) 64.059 296.8 300.2 248.1 Trixido de S SO3(g) 80.058 395.8 371.0 256.8 Agua H2O(g) 18.016 241.8 228.6 188.7 Agua H2O(l) 18.016 285.8 237.2 69.9 Metano CH4(g) 16.043 74.8 50.8 186.2 Etano C2H6(g) 30.070 84.7 32.9 229.5 Propano C3H8(g) 44.097 103.8 23.5 269.9 n-Butano C4H10(g) 58.124 126.2 17.2 310.1 n-Pentano C5H12(g) 72.151 146.4 8.37 348.9 n-Hexano C6H14(g) 86.178 167.3 28.0 388.0 n-Heptano C7H16(g) 100.205 187.8 8.12 427.8 n-Octano C8H18(g) 114.232 208.4 16.5 466.7 n-Octano C8H18(l) 114.232 250.0 6.61 360.8 n-Dodecano C12H26(g) 179.34 290.9 50.1 622.5 Nitrometano CH3NO2 61.043 113.1 14.4 171.8 Metanol CH4O(l) 32.043 238.7 166.4 126.8 Etanol C2H6O(g) 46.070 235.0 168.3 282.4 Acetileno C2H2(g) 26.038 226.7 209.2 201.0 Etileno C2H4(g) 28.054 52.5 68.2 219.5 Benceno C6H6(g) 78.114 83.0 129.8 269.6

* Fuente: WARK, K., Termodinmica, McGraw Hill, 1991; National Bureau of Standards (US Deparment of Comerce), Technical notes 270-3, 270-4 and Circular 500.


TTAABBLLAA AA..1155

Poder calorfico inferior, calor de vaporizacin, volumen molar y punto de ebullicin normal de algunos combustibles a 298 K y 1 atm.

iq , kJ/mol; l , kJ/mol; v , cm3/mol; Tb , K

Sustancia Frmula iq l v Tb Hidrgeno H2(g) 241.8 ----- ----- 20.4 Carbono C(s) 393.6 ----- ----- ----- Monxido de C CO(g) 283.0 ----- ----- 81.7 Metano CH4(g) 802.2 ----- ----- 112 Etano C2H6(g) 1430 5.02 ----- 185 Propano C3H8(g) 2043 14.8 ----- 231 n-Butano C4H10(g) 2658 21.1 ----- 273 n-Pentano C5H12(g) 3293 26.4 115.2 309 n-Hexano C6H14(l) 3857 31.5 130.5 341 n-Heptano C7H16(l) 4466 36.7 145.5 371 n-Octano C8H18(l) 5074 41.5 162.6 399 n-Nonano C9H20(l) 5672 n-Decano C10H22(l) 6282 51.0 n-Undecano C11H24(l) 6894 n-Dodecano C12H26(l) 7518 61.3 222.0 489 Nitrometano CH3NO2(l) 643.2 38.4 53.6 Cetano C16H34(l) 9944 Benceno C6H6(l) 3131 34.0 88.9 353 Metanol CH4O(l) 637.1 37.9 40.4 338 Etanol C2H6O(l) 1233 42.3 58.4 351 Acetileno C2H2(g) 1256 21.6 41.9 190 Gasolinaa C7H17(l) 4495 38.5 154.0 ----- Querosenoa C12.3H22.4(l) 7350 44.9 186.8 ----- Diesela C14.4H24.9(l) 8501 74.1 233.0 ----- Agua H2O(l) 0 44.0 18.0 373

a Estimado para combustible tpico.

APNDICE A 779

TTAABBLLAA AA..1166

Entalpa y energa interna sensibles y entropa absoluta del CO2 como gas ideal* 52.393 ====fh kJ/mol; M = 44.011 g/mol

T, K; h y u , kJ/mol; s , J/mol/K

T h u s T h u s 100

6.155 6.986 181.067 2000 91.450 74.820 309.210 200

3.376 5.039 200.024 2100 97.500 80.039 312.160 298 0.000

2.478 213.685 2200 103.575 85.282 314.988 300 0.069

2.428 213.915 2300 109.671 90.547 317.695 400 4.008 0.682 225.225 2400 115.788 95.832 320.302 500 8.314 4.157 234.814 2500 121.926 101.139 322.808 600 12.916 7.927 243.199 2600 128.085 106.466 325.222 700 17.761 11.941 250.663 2700 134.256 111.806 327.549 800 22.815 16.163 257.408 2800 140.444 117.162 329.800 900 28.041 20.558 263.559 2900 146.645 122.532 331.975

1000 33.405 25.090 269.215 3000 152.862 127.917 334.084 1100 38.894 29.748 274.445 3100 159.092 133.316 336.126 1200 44.484 34.506 279.307 3200 165.391 138.783 338.109 1300 50.158 39.349 283.847 3300 171.586 144.147 340.034 1400 55.907 44.266 288.106 3400 177.849 149.578 341.904 1500 61.714 49.242 292.114 3500 184.121 155.019 343.720 1600 67.580 54.276 295.901 3600 190.405 160.471 345.490 1700 73.492 59.357 299.482 3700 196.698 165.933 347.213 1800 79.442 64.475 302.884 3800 202.999 171.402 348.895 1900 85.429 69.631 306.122 3900 209.313 176.885 350.536

* Fuente: JANAF Thermochemical Tables, NSRDS-NBS-37, 1971.


TTAABBLLAA AA..1177

Entalpa y energa interna sensibles y entropa absoluta del CO como gas ideal* 53.110 ====fh kJ/mol; M = 28.011 g/mol


T h u s T h u s 100

5.828 6.660 165.339 2000 56.739 40.109 258.600 200

2.866 4.529 185.878 2100 60.375 42.8913 260.370 298 0.000

2.478 197.543 2200 64.019 45.726 262.065 300 0.054

2.441 197.723 2300 67.676 48.551 263.692 400 2.975

0.351 206.125 2400 71.346 51.390 265.253 500 5.929 1.771 212.719 2500 75.023 54.235 266.755 600 8.941 3.952 218.204 2600 78.714 57.095 268.203 700 12.021 6.200 222.953 2700 82.408 59.957 269.596 800 15.175 8.523 227.162 2800 86.115 62.833 270.943 900 18.397 10.913 230.957 2900 89.826 65.712 272.240

1000 21.686 13.371 234.421 3000 93.542 68.597 273.508 1100 25.033 15.886 237.609 3100 97.270 71.495 274.730 1200 28.426 18.448 240.563 3200 100.998 74.390 275.914 1300 31.865 21.055 243.316 3300 104.734 77.294 277.064 1400 35.338 23.697 245.889 3400 108.479 80.208 278.182 1500 38.848 26.375 248.312 3500 112.223 83.120 279.265 1600 42.384 29.080 250.592 3600 115.976 86.042 280.324 1700 45.940 31.804 252.751 3700 119.734 88.968 281.353 1800 49.522 34.555 254.797 3800 123.495 91.898 282.357 1900 53.124 37.325 256.743 3900 127.261 94.832 283.332


APNDICE A 781

TTAABBLLAA AA..1188

Entalpa y energa interna sensibles y entropa absoluta del H2O como gas ideal* 820.241 ====fh kJ/mol; M = 18.016 g/mol


T h u s T h u s 100

6.615 7.446 152.281 2000 72.689 56.059 264.571 200

3.280 4.943 175.377 2100 77.831 60.369 267.081 298 0.000

2.478 188.724 2200 83.036 64.743 269.500 300 0.063

2.432 188.929 2300 88.295 69.170 271.839 400 3.452 0.126 198.673 2400 93.604 73.648 274.098 500 6.920 2.762 206.413 2500 98.964 78.176 276.286 600 10.498 5.509 212.928 2600 104.370 82.751 278.408 700 14.184 8.363 218.610 2700 109.813 87.362 280.462 800 17.991 11.339 223.693 2800 115.294 92.012 282.453 900 21.924 14.440 228.321 2900 120.813 96.699 284.391

1000 25.978 17.663 232.597 3000 126.361 101.416 286.273 1100 30.167 21.020 236.584 3100 131.942 106.167 288.102 1200 34.476 24.498 240.333 3200 137.553 110.945 289.884 1300 38.903 28.093 243.877 3300 143.189 115.749 291.616 1400 43.447 31.806 247.241 3400 148.854 120.583 293.307 1500 48.095 35.622 250.450 3500 154.540 125.437 294.955 1600 52.844 39.540 253.513 3600 160.247 130.313 296.566 1700 57.685 43.549 256.450 3700 165.975 135.209 298.135 1800 62.609 47.642 259.262 3800 171.724 140.127 299.666 1900 67.613 51.814 261.969 3900 177.494 145.065 301.164



TTAABBLLAA AA..1199

Entalpa y energa interna sensibles y entropa absoluta del H2 como gas ideal* 0.0 ====fh kJ/mol; M = 2.016 g/mol


T h u s T h u s 100

5.293 6.124 102.035 2000 52.932 36.302 188.297 200

2.770 4.403 119.328 2100 56.379 38.917 189.979 298 0.000

2.478 130.574 2200 59.860 41.567 191.598 300 0.054

2.441 130.754 2300 63.371 44.246 193.159 400 2.958

0.368 139.105 2400 66.915 46.959 194.669 500 5.883 1.725 145.628 2500 70.492 49.704 196.125 600 8.812 3.823 150.967 2600 74.091 52.472 197.539 700 11.749 5.928 155.498 2700 77.718 55.267 198.907 800 14.703 8.051 159.440 2800 81.370 58.088 200.234 900 17.682 10.198 162.950 2900 85.044 60.930 201.527

1000 20.686 12.371 166.113 3000 88.743 63.798 202.778 1100 23.723 14.576 169.008 3100 92.458 66.683 203.995 1200 26.794 16.816 171.682 3200 96.199 69.591 205.183 1300 29.907 19.097 174.172 3300 99.960 72.520 206.342 1400 33.062 21.421 176.510 3400 103.738 75.467 207.468 1500 36.267 23.794 178.724 3500 107.541 78.438 208.572 1600 39.522 26.218 180.820 3600 111.361 81.427 209.648 1700 42.815 28.679 182.820 3700 115.206 84.440 210.702 1800 46.150 31.183 184.724 3800 119.064 87.467 211.731 1900 49.522 33.723 186.548 3900 122.947 90.518 212.740


APNDICE A 783

TTAABBLLAA AA..2200

Entalpa y energa interna sensibles y entropa absoluta del O2 como gas ideal* 0.0 ====fh kJ/mol; M = 32.00 g/mol


T h u s T h u s 100

5.700 6.530 173.728 2000 59.199 42.569 268.655 200

2.853 4.516 193.439 2100 62.986 45.524 270.504 298 0.000

2.478 205.033 2200 66.802 48.509 272.278 300 0.054

2.441 205.213 2300 70.634 51.509 273.981 400 3.029

0.297 213.765 2400 74.492 54.536 275.625 500 6.088 1.930 220.589 2500 78.375 57.587 277.207 600 9.247 4.258 226.346 2600 82.274 60.655 278.738 700 12.502 6.681 231.363 2700 86.199 63.748 280.219 800 15.841 9.189 235.814 2800 90.144 66.862 281.654 900 19.246 11.762 239.827 2900 94.111 69.997 283.048

1000 22.707 14.392 243.475 3000 98.098 73.153 284.399 1100 26.217 17.070 246.818 3100 102.102 76.327 285.713 1200 29.765 19.787 249.906 3200 106.127 79.519 286.989 1300 33.351 22.541 252.776 3300 110.169 82.729 288.232 1400 36.966 25.325 255.454 3400 114.232 85.961 289.445 1500 40.610 28.137 257.969 3500 118.307 89.204 290.625 1600 44.279 30.975 260.337 3600 122.399 92.465 291.780 1700 47.970 33.834 262.575 3700 126.507 95.741 292.905 1800 51.689 36.722 264.701 3800 130.629 99.032 294.005 1900 55.434 39.635 266.726 3900 134.762 102.333 295.077



TTAABBLLAA AA..2211

Entalpa y energa interna sensibles y entropa absoluta del N2 como gas ideal* 0.0 ====fh kJ/mol; M = 28.0134 g/mol


T h u s T h u s 100

5.770 6.601 159.703 2000 56.141 39.511 251.969 200

2.858 4.521 179.879 2100 59.748 42.286 253.726 298 0.000

2.478 191.502 2200 63.371 45.078 255.412 300 0.054

2.441 191.682 2300 67.008 47.883 257.027 400 2.971

0.355 200.071 2400 70.651 50.695 258.580 500 5.912 1.754 206.631 2500 74.312 53.524 260.073 600 8.883 3.894 212.066 2600 77.981 56.362 261.513 700 11.937 6.116 216.756 2700 81.659 59.208 262.902 800 15.046 8.394 220.907 2800 85.345 62.063 264.241 900 18.221 10.737 224.647 2900 89.036 64.922 265.529

1000 21.460 13.145 228.057 3000 92.738 67.793 266.793 1100 24.757 15.610 231.199 3100 96.445 70.670 268.006 1200 28.108 18.130 234.116 3200 100.161 73.553 269.186 1300 31.480 20.670 236.831 3300 103.885 76.445 270.332 1400 34.936 23.295 239.375 3400 107.608 79.337 271.445 1500 38.405 25.932 241.768 3500 111.340 82.237 272.525 1600 41.903 28.599 244.028 3600 115.081 85.147 273.579 1700 45.430 31.294 246.166 3700 118.817 88.051 274.604 1800 48.982 34.015 248.195 3800 122.570 90.973 275.604 1900 52.551 36.752 250.128 3900 126.319 93.890 276.579


APNDICE A 785

TTAABBLLAA AA..2222

Entalpa sensible de algunos combustibles gaseosos a baja presin T, K; h , kJ/mol

T CH4 C2H6 C3H8 C4H10 C8H18 C2H4 CH3OH 200

3.372 4.615 6.326 8.532 16.201 3.699 298 0.000 0.000 0.000 0.000 0.000 0.000 0.000 300 0.067 0.101 0.034 0.184 0.334 0.079 0.083 400 3.871 6.000 8.536 11.372 21.798 4.889 4.836 500 8.222 13.184 18.883 25.074 48.157 10.670 10.384 600 13.176 21.556 30.949 40.974 78.868 17.332 16.719 700 18.711 30.970 44.547 58.839 113.302 24.764 23.765 800 24.803 41.346 59.442 78.337 150.916 32.855 31.438 900 31.401 52.560 75.467 99.257 190.684 41.509 39.660

1000 38.476 64.484 92.454 121.390 232.923 50.662 48.383 1100 45.966 77.036 110.362 144.653 60.255

* Fuente: Adaptada de J.B. Jones y R.E. Dugan, Ingeniera Termodinmica, Prentice Hall, 1997


TTAABBLLAA AA..2233

Logaritmos en base 10 de la constante de equilibrio Kp para algunas reacciones* Reacciones numeradas: (1) CO2 CO + O2

(2) H2O H2 + O2 (3) CO2 + H2 CO + H2O

T, K log Kp T, K

log Kp (1) (2) (3) (1) (2) (3)

298 45.07 40.05 5.018 2400 1.679 2.443 0.764

500 25.03 22.89 2.139 2500 1.440 2.224 0.784

1000 10.22 10.06 0.159 2600 1.219 2.021 0.802

1200 7.764 7.899 0.135 2800 0.825 1.658 0.833

1400 6.014 6.347 0.333 3000 0.485 1.343 0.858

1500 5.316 5.725 0.409 3100 0.332 1.201 0.869

1600 4.706 5.180 0.474 3200 0.189 1.067 0.878

1700 4.169 4.699 0.530 3300 0.054 0.942 0.888

1800 3.693 4.270 0.577 3400 0.071 0.824 0.895

1900 3.267 3.886 0.619 3500 0.190 0.712 0.902

2000 2.884 3.540 0.656 3600 0.302 0.607 0.909

2100 2.539 3.227 0.688 3700 0.408 0.507 0.915

2200 2.226 2.942 0.716 3800 0.508 0.413 0.921

2300 1.940 2.682 0.742 3900 0.603 0.323 0.926

* Valores adaptados de JANAF Thermochemical Tables, US National Bureau of Standards, 1985.

APNDICE A 787

TTAABBLLAA AA..2244

Flujo isoentrpico unidimensional de un gas ideal con k=1.4

M p0 /p 0 / T0 /T A/A* 0.1 1.007 1.005 1.002 5.820 0.2 1.028 1.020 1.008 2.963 0.3 1.065 1.046 1.018 2.035 0.4 1.117 1.082 1.032 1.590 0.5 1.187 1.130 1.050 1.340 0.6 1.276 1.190 1.073 1.188 0.7 1.388 1.263 1.099 1.094 0.8 1.525 1.351 1.129 1.038 0.9 1.693 1.455 1.163 1.009 1.0 1.895 1.577 1.201 1.000 1.1 2.137 1.718 1.244 1.008 1.2 2.428 1.882 1.290 1.030 1.3 2.774 2.069 1.341 1.066 1.4 3.186 2.284 1.395 1.115 1.5 3.675 2.529 1.453 1.176 1.6 4.255 2.807 1.516 1.250 1.7 4.941 3.123 1.582 1.337 1.8 5.751 3.480 1.653 1.438 1.9 6.706 3.882 1.727 1.554 2.0 7.830 4.335 1.806 1.685 2.1 9.149 4.844 1.889 1.834 2.2 10.70 5.415 1.975 2.001 2.3 12.50 6.052 2.066 2.188 2.4 14.62 6.764 2.161 2.397 2.5 17.08 7.558 2.259 2.629 2.6 19.94 8.440 2.362 2.886 2.7 23.25 9.418 2.469 3.171 2.8 27.09 10.50 2.580 3.485 2.9 31.53 11.70 2.695 3.832 3.0 36.64 13.02 2.813 4.213 3.5 75.93 21.89 3.468 6.739 4.0 150.8 35.70 4.224 10.61 5.0 529.1 88.18 6.000 25.00 6.0 1579 192.6 8.200 53.18 8.0 9763 707.5 13.80 190.1

10.0 42440 2021 21.00 535.9


TTAABBLLAA AA..2255

Flujo unidimensional a travs de un shock normal de un gas ideal con k=1.4

Mx py /px y /x Ty /Tx My p0y /p0x 1.01 1.0235 1.0167 1.0067 0.9901 1.9171 1.1 1.2452 1.1688 1.0653 0.9118 2.1351 1.2 1.5138 1.3410 1.1288 0.8422 2.4102 1.3 1.8057 1.5147 1.1921 0.7861 2.7168 1.4 2.1210 1.6882 1.2564 0.7399 3.0530 1.5 2.4596 1.8601 1.3223 0.7013 3.4177 1.6 2.8216 2.0291 1.3906 0.6687 3.8100 1.7 3.2070 2.1944 1.4614 0.6408 4.2296 1.8 3.6157 2.3552 1.5352 0.6168 4.6760 1.9 4.0477 2.5109 1.6120 0.5960 5.1490 2.0 4.5031 2.6611 1.6922 0.5778 5.6485 2.1 4.9819 2.8056 1.7757 0.5617 6.1743 2.2 5.4840 2.9440 1.8627 0.5475 6.7263 2.3 6.0095 3.0765 1.9533 0.5349 7.3044 2.4 6.5583 3.2031 2.0475 0.5236 7.9086 2.5 7.1305 3.3237 2.1454 0.5135 8.5389 2.6 7.7260 3.4385 2.2469 0.5044 9.1951 2.7 8.3449 3.5477 2.3522 0.4962 9.8773 2.8 8.9871 3.6514 2.4613 0.4888 10.5854 2.9 9.6527 3.7499 2.5741 0.4820 11.3195 3.0 10.342 3.8434 2.6907 0.4758 12.0794 4.0 18.516 4.5511 4.0683 0.4357 21.1022 5.0 29.000 5.0000 5.8000 0.4152 32.653

10.0 116.50 5.7143 20.387 0.3876 129.22

Documents

Tabla de propiedades